% Load the parameters that lead to multiplicity
global g rho sigma PStar taub tauh k l tau tauBarBench zBarBench zTildeBench
global z0_M
loadVariables;
% First load the baseline parameters

% Then change them to create multiplicity
% Raise optimists' leverage while keeping baseline alpha the same. 
l=0.94;
k=k;
% Adjust their taub to keep tauBar_0 unchanged
taub = fsolve(@(tb) tb*k*(1-l)+tauh*(1-k*(1-l)) - tauBarBench,taub);

tau = taub*k+tauh*(1-k);
ph = exp(rho + g - sigma^2/tauh);

assert( tauBarBench>= sigma^2/(rho+g));
zBar = fsolve(@(z) tau - k*l/z*(taub-tauh) -  sigma^2/(rho+g),1);
zTilde = l/ph;

% Check the condition for multiplicity
assert(zTilde>zBar);

% Set z0_M in the middle of zBar and zTilde
z0_M = 0.5*zBar + 0.5*min(1,zTilde);